The simulation models are built up to analyze the Cp of the parallel matrix systems and compare with that of one single Savonius wind rotor. The dimensions of the simulation model are shown in Tables 3.1 and 3.2. Regarding the boundary conditions, the wind velocity is set to be 7 m/s and 14 m/s, in addition the variation of tip-speed ratio is constrained in the range of 0.4 through 1.2. The predicted Cps of one single Savonius wind rotor and the parallel matrix systems are shown in Table 4.11 and Fig. 4.26. The highest Cp of one single Savonius wind rotor occurs at 0.8 tip-speed ratio and the one of the parallel matrix system with four Savonius wind rotors occurs while the tip-speed ratio is 0.9. In present study, the average Cp of the parallel matrix system with four Savonius wind rotors is 2.07 times higher than that in one single Savonius wind rotor. However, in Huang’s predictions [2], which investigates the parallel matrix system with four Savonius wind rotors, the corresponding Cp was 1.46 times higher than that in one single Savonius wind rotor; in Feng’s predictions [1], which investigates the parallel matrix system with three Savonius wind rotors, the corresponding Cp is predicted to be 1.9 times higher than that in one single Savonius wind rotor.
Table 4.11 and Fig. 4.26 also show that the Cps of one single Savonius
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wind rotor in this study are lower than that in Huang [2] at all different tip-speed ratios, but the Cps for the parallel matrix system with four Savonius wind rotors are higher than that in Huang [2]. The reasons that lead to the discrepancy are the different wind blade structures. In addition, the Cps for both single rotor and matrix system at each tip-speed ratio in the present study are lower compared to the results from Feng [1]. The reasons that bring about the discrepancy are the different distances between each rotor.
Table 4.11 Predicted Cps at different Tip-speed Ratios in 2-D simulations:
(a) one single rotor (b) parallel matrix systems (a)
Tip-speed
This research also includes one single Savonius wind rotor, the parallel matrix system with four Savonius wind rotors and the parallel matrix system with ten Savonius wind rotors. Fig. 4.27 shows that the Cps of one single Savonius wind rotor, the parallel matrix system with four Savonius wind rotors and the parallel matrix system with ten Savonius wind rotors. These systems are in the wind speeds of 7m/s and the tip speed ratios ranged from 0.4 to 1.2. The average Cp of the parallel matrix system with ten Savonius wind rotors is 2.25 times higher than that in one single Savonius wind rotor and the average Cp of the parallel matrix system with four Savonius wind rotors is 2.07 times higher than that in one single Savonius wind rotor. However, the average Cp of the parallel matrix system with ten Savonius wind rotors is 1.08 times higher than that in the parallel matrix system with four Savonius wind rotors. It also reveals that parallel matrix systems apparently have higher performance than one single
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rotor.
Furthermore, the power output can be derived from Cp as follows:
Cp = W 12 ρAv3
⇒ W = Cp ⋅ (1
2 ρAv3)
By using the above equation, the maximums of average power output of Savonius wind rotor in the three conditions, the parallel matrix systems with phase angle difference 90° and one single Savonius wind rotor, are calculated and the results are listed in Table 4.12.
Table 4.12 The maximum of average power output of the parallel matrix systems and one Single Savonius wind rotor
Condition Wind Direction
Wind Speed
Matrix System with Ten Savonius Wind
Rotors
14 252.18
θ=37° 7 46.35
14 427.52
θ=53° 7 57.3
14 520.24
θ=90° 7 82.87
14 700.46
From the above table, it can be seen that the average power output of the parallel matrix systems are higher than the average power output of one single Savonius wind rotor. The reason is that the performance enhancement in the parallel matrix system depends on the positive interactions between wind rotors.
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(a)
(b)
(c)
Fig. 4.1 Schematics of Savonius wind rotor geometry: (a) present thesis; (b) Feng [1]; (c) Huang [2]
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(a)
(b)
Fig. 4.2 The 2D simulation of one single Savonius wind rotor comparing with Feng’s predictions [1], Huang’s predictions [2] and experimental measurements by Howell et al. [12] in: (a) wind speed 7 m/s; (b) wind speed
14 m/s
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Fig. 4.3 The performance of one single Savonius wind rotor
(a)
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(b)
Fig. 4.4 Velocity vector distribution around one single Savonius wind rotor at α=100° in wind speed: (a) 7m/s; (b) 14m/s
α x y
Wind
Fig. 4.5 The defined angle α of rotating wind blade relative to the initial angle
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Fig 4.6 Torque curve of one single Savonius wind rotor with wind speed 7 m/s and tip-speed ratio 0.8 in a rotation
(a)
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(b)
Fig. 4.7 Static pressure field around one single Savonius wind rotor in 2-D simulation at: (a) α=20°; (b) α=100°
(a)
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(b)
Fig. 4.8 Velocity vector distribution around one single Savonius wind rotor in 2-D simulation at: (a) α=20°; (b) α=100°
Fig. 4.9 Phase-averaged pressure difference from the average pressure field [14]
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(a)
(b)
Fig. 4.10 Velocity vector distribution around the parallel matrix system with four Savonius wind rotors in wind speed: (a) 7m/s; (b) 14m/s
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Fig. 4.11 Torque curves of the parallel matrix system with four Savonius wind rotors and one single Savonius wind rotor
Fig. 4.12 Static pressure field around the parallel matrix system with four Savonius wind rotors
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Fig. 4.13 Velocity vector distribution around the parallel matrix system with four Savonius wind rotors
Fig. 4.14 Streamlines around the parallel matrix system with four Savonius wind rotors at wind speed 7 m/s and TSR 0.9
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Fig. 4.15 Comparison of the parallel matrix system with four Savonius wind rotors and one single Savonius wind rotor
(a)
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(b)
Fig. 4.16 Velocity vector distribution around the parallel matrix system with ten Savonius wind rotors in wind speed: (a) 7m/s; (b) 14m/s
Fig. 4.17 Torque curves of the parallel matrix system with ten Savonius wind rotors and one single Savonius wind rotor
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Fig. 4.18 Static pressure field around the parallel matrix system with ten Savonius wind rotors
Fig. 4.19 Velocity vector distribution around the parallel matrix system with ten Savonius wind rotors
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Fig. 4.20 Streamlines around the parallel matrix system with ten Savonius wind rotors at wind speed 7 m/s and TSR 0.7
Fig. 4.21 Comparison of the parallel matrix system with ten Savonius wind rotors and one single Savonius wind rotor
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Fig. 4.22 Three-rotor with phase angle difference 90° in different wind directions [1]
Fig. 4.23 the parallel matrix system with ten Savonius wind rotors in different wind directions
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(a)
(b)
86
(c)
(d)
Fig. 4.24 Velocity vector distribution around the ten Savonius wind rotors with a change of wind direction θ (a) θ = 0°; (b) θ = 37°; (c) θ = 53°; (d) θ =
90°
87
(a)
(b)
88
(c)
(d)
Fig. 4.25 Static pressure field around the ten Savonius wind rotors with a change of wind direction θ (a) θ = 0°; (b) θ = 37°; (c) θ = 53°; (d) θ = 90°
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(a)
(b)
Fig. 4.26 Predicted Cps at different Tip-speed Ratios in 2-D simulations: (a) one single rotor; (b) parallel matrix system
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Fig. 4.27 Comparison of the parallel matrix system with ten Savonius wind rotors, the parallel matrix system with four Savonius wind rotors and one
single Savonius wind rotor
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